Yang–Mills-like field theories are developed using both division quaternion and octonion algebras. Quaternionic field theory is the same as the Yang–Mills gauge theory. The octonionic field theory is an expansion from a similar field theory built with split octonions algebra that uses a complex-form basis as proposed by Gunaydin and Gursey (J Math Phys 14:1651, 1973), now with division octonions. This proposed octonionic field theory is the last possible field theory built using the division algebra of octonions, as permitted by the Hurwitz theorem. The interpretation of this “octonionic field” is not straightforward, except that it is similar to the quaternionic Yang–Mills field. A possible interpretation for this octonionic field theory for spin-1/2 particles is proposed in terms of quantum mechanics.

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基于四元数和八元数代数的Yang-Mills类场论

类似于杨-米尔斯的场论是使用四元数除法和八元数代数发展的。四元离子场理论与Yang-Mills规范理论相同。牛顿离子场理论是对类似的场理论的扩展，该场论是用分裂八音子代数建立的，该理论使用了Gunaydin和Gursey（J Math Phys 14：1651，1973）提出的复数形式基础，现在有了分割正弦子。如Hurwitz定理所允许的那样，这种拟议的正电子场理论是使用正电子的分代数建立的最后一种可能的场理论。除了与四元的Yang-Mills场相似外，对“渗透子场”的解释并不简单。从量子力学的角度出发，提出了对自旋1/2粒子的此张子场理论的可能解释。